The work of friction forces - and - the total work of systems

In summary, the conversation discusses two conceptual problems related to friction and work. Problem 1 discusses whether friction can ever do positive work, and Problem 2 discusses the total work done in a system involving a rope and a box. The speakers provide different perspectives and examples to support their arguments, but the main question remains unanswered. Ultimately, the conversation highlights the complexity of the relationship between friction and work, with no clear consensus on the answer.
  • #1
Bonulo
46
0
I've been given two conceptual problems that I can't quite crack, at least, I'm not sure that I'm cracking them:

Problem 1
When a box is moving across a rough surface the friction force does negative work. Can a friction force ever do positive work? If yes, give an example, if no, explain why.
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I've aserted, in my so-far solution, that friction force can never do positive work, based on rudimentary readings on the perpetuum mobile (the eternity machine). The main reason for it's unattainability is the existence of friction, thus I don't think friction can do positive work. Since it would result in an increase in kinetic energy, without having anything to transform it from. I am, however, not sure that the arguments hold. So I'm now chasing either the right arguments or the one example that will prove friction force can do positive work.

If a box is on a conveyor belt, and the conveyor belt is turned on, and thus accelerates, the box stays for a while (because of static friction), but is accelerating along with the belt. At some point the box starts sliding across the belt, and there is kinetic friction. But - since the absence of kinetic friction would cause the box to stay in it's initial position (with respect to the inertial coordinate system - the Earth), isn't the existence of kinetic friction then directed like the movement itself, thus doing positive work on the box?


Problem 2
A rope is used to pull a box, which therefore accelerates. According to Newtons 3rd Law the box pulls the rope with a force as big but with opposite direction. Is the total work done, as mentioned in the work-energy theorem, then 0? If it is, how can you change the kinetic energy of a body?
-----

The work-energy theorem says that W.tot=K2-K1=deltaK. But this applies to the work of one body on another body, not to the total work of a system. If I pull the box, I do the work W.tot, which it counters with -W.tot (the same size force, with the opposite direction). The total value of work will then, always, be 0, since W.tot+(-W.tot) = 0. But isn't that addition quite irrelevant? The kinetic energy of both bodies has been altered, which can easily by seen by using the work-energy theorem.

Is this some kind of trick question?


Any help would be muchly appreciated. The assignment's due tomorrow.
 
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  • #2
Comment on 1

The friction force is a resistive force - it is directed as to oppose relative motion - not motion. So I don't think that the solution is in the definition itself. But does the conveyor belt theory solve the problem? Or is it invalid?
 
  • #3
Comment on 2:

If a push lasts for a while, the contact Force transfers momentum through the contact Area from one object to the other. This is guaranteed by the definition of momentum, so we know we can use momentum conservation for a system.

If you push for a ways, the Force transfers Energy from one object to the other. This is not a trick question - if it did NOT work this way, we could not use the Energy conservation approach to describe mechanical systems!

Comment on 1's box-on-conveyor-belt:

The Work done by friction on the box is positive/negative according to :
a) the box's reference frame
b) the conveyor belt's reference frame
How about the Work done by friction on the conveyor belt in
a) and b)?
 
  • #4
On 2:
I don't quite follow you - if you were aiming at a clear response to the problem itself. Is the total work W zero? I know kinetic energy is changed for each object, but what do you think the question means?


On 1:
I'm just using the Earth as a frame of reference. If I answered if friction can or can't do positive work according to a not-inertial frame of reference - then I wouldn't have answered the question, would I? Since we always use inertial frames of reference.

I made a Google search on the string "friction does positive work" and found this: http://www.artsci.gmcc.ab.ca/courses/enph131oa/sem08_w05_solutions.pdf [Broken]

A professor from MacEwan Faculty of Arts & Science claims that friction, in a situation similar to mine, does positive work. But I also found some professors who claimed otherwise. Which is true?

(a co-student, to add to the confusion, says that another co-student asked our professor, and that he said friction can't do positive work - I just don't know if I can trust this 3rd hand statement to be true)
 
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  • #5
Bonulo said:
On 2:
I don't quite follow you - if you were aiming at a clear response to the problem itself. Is the total work W zero? I know kinetic energy is changed for each object, but what do you think the question means?On 1:
I'm just using the Earth as a frame of reference. If I answered if friction can or can't do positive work according to a not-inertial frame of reference - then I wouldn't have answered the question, would I? Since we always use inertial frames of reference.

I made a Google search on the string "friction does positive work" and found this: http://www.artsci.gmcc.ab.ca/courses/enph131oa/sem08_w05_solutions.pdf [Broken]

A professor from MacEwan Faculty of Arts & Science claims that friction, in a situation similar to mine, does positive work. But I also found some professors who claimed otherwise. Which is true?

(a co-student, to add to the confusion, says that another co-student asked our professor, and that he said friction can't do positive work - I just don't know if I can trust this 3rd hand statement to be true)
Work is a scalar quantity but it is derived from the dot product of two vectors - force and distance:

[tex]W = \int \vec{F} \cdot d\vec{x} = \int Fdxcos\theta[/tex]

where [itex]\theta[/itex] is the angle between the force and the direction of the change in position.

Negative work results when the direction of the force is opposite to the direction of motion. What direction is friction relative to the direction of motion? That should tell you whether friction always does negative work.

AM
 
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  • #6
No. I know all that stuff already. Friction has the opposite direction of RELATIVE motion, not motion (i.e. motion relative to the inertial frame of reference). I want the .pdf-file solution to be validated or invalidated. If it's valid, friction can do positive work, if it's not, friction can't.

Aw. I've asked everywhere now, and get the same, rudimentary responses or hints all the time. This is a basic university physics course, is it supposed to be this hard? :/
 
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  • #7
Bonulo said:
I made a Google search on the string "friction does positive work" and found this: http://www.artsci.gmcc.ab.ca/courses/enph131oa/sem08_w05_solutions.pdf [Broken]

A professor from MacEwan Faculty of Arts & Science claims that friction, in a situation similar to mine, does positive work. But I also found some professors who claimed otherwise. Which is true?

(a co-student, to add to the confusion, says that another co-student asked our professor, and that he said friction can't do positive work - I just don't know if I can trust this 3rd hand statement to be true)
I would say that the paper you have linked to is wrong or, at best, is unclear in identifying the frame of reference in which force and displacement is to be measured.

Static friction force, like any force, comes in pairs: an applied force and a static friction reaction force. They are always equal and opposite. The static friction force is a reaction to the applied force. If you remove the applied force, the static friction force goes to zero.

The force that the box exerts on my hand when I push on the box (with no relative motion between my hand and the box) is a similar reaction force. It is the force of my hand that does positive work on the box as measured in the initial rest frame of the box. The reaction force of the box on my hand does negative work on my body.

It is incorrect to say that the reaction force of the box on my hand does positive work on the box. But that is what this paper appears to be saying.

AM
 
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  • #8
Is it? The paper says that a block that's dropped unto a conveyor belt will be acted upon by a kinetic friction force - from the surface of the belt - which seeks to keep the block on the belt, thus increasing its speed (and kinetic energy) relative to any point on the planet Earth. Is that wrong?
 
  • #9
hmm..

I really think the answer is NO (friction can't do positive work)
 
  • #10
Huh? All of a sudden? But why? You're challenged to shoot down the .pdf-solution. If you can't, then your answer's at best imperfect with respect to argument-sufficiency.
 
  • #11
the pdf-solution

relative to the belt, the block does not increase its kinetic energy.
 
  • #12
msn?

do you have msn bonulo?

Mine is erikandr(at)gmail.com
 
  • #13
No, but why is that relation even relevant?
 
  • #14
Bonulo said:
No, but why is that relation even relevant?
In the case of the box landing on the moving conveyor (or a moving box landing on a stopped conveyor), the force of friction causes the box and belt to eventually move together - an inelastic collision - so energy is lost to the system. The energy that is lost is heat, due to friction. So friction does negative work in the sense that it causes a loss of mechanical energy.

If the conveyor belt was unpowered the box would slow the conveyor. Although it would speed up the box, the loss of energy of the conveyor would be greater than the gain in energy of the box - due to friction loss.

AM
 
  • #15
I don't see what's wrong with the paper talking about the box on the conveyor belt. One should be careful in stating that the static friction force TRANSMITS positive work to the box. The friction is not the the source of the energy, but it transmits the energy that the motor sends to the conveyor belt to account for the increase in mass moving at a constant velocity. Would you agree with that AM?
 
  • #16
cyrusabdollahi said:
I don't see what's wrong with the paper talking about the box on the conveyor belt. One should be careful in stating that the static friction force TRANSMITS positive work to the box. The friction is not the the source of the energy, but it transmits the energy that the motor sends to the conveyor belt to account for the increase in mass moving at a constant velocity. Would you agree with that AM?
I don't think it is quite correct to describe the force as 'transmitting' energy. Friction provides a mechanical linkage between two objects. That linkage allows two objects to apply equal and opposite forces to each other. This allows mechanical energy to pass from one object to the other. But it is a linkage that does not conserve mechanical energy. Kinetic friction always reduces the mechanical energy of a system.

AM
 
  • #17
Yes, but I am talking static friction, which allows the block to accelerate up to speed v_conveyor belt when it falls onto it.

If the block simply falls straight down onto the belt, it has zero velocity in the x direction. So when it falls onto the belt, it will pick up speed until the speeds match. So there has to be a net force acting on the block to cause it to accelerate. Thats what the static friction does. And that force acts for some amount of time, and over some distance. So it supplies some amount of work to the box.
 
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  • #18
The work done is simply given by [itex] \int F.ds [/itex] . Work is done by the foce and we consider the displacement as the distance moved by the point of application of force , limiting c0ondition being that the body is rigid and each point move the same distance. Because friction is peculiarly known to oppose motion, in general motions , this force does negative work . Consider your feet when walking , you push the ground backwards the friction force directs itself forward and as a result you move forward. What do you think in this case? Does the friction do negative work? ... Consider a case of rolling without slipping body on a rough surface , so when it is 'accelerating- rotationally' . the friction directs itself forward to give an opposing torque , but the wheel keeps moving forward till it comes to rest , so for that time does friction does +ve work? ...think.

BJ
 
  • #19
Im sorry Dr. Brain, I don't understand what your saying. Are you talking about a wheel that's rolling to a rest? That is kinetic friction slowing it down and it does negative work, but that's not what I am talking about. I am dealing with static friction.

Because friction is peculiarly known to oppose motion, in general motions , this force does negative work .

Thats not true in general.
 
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  • #20
cyrusabdollahi said:
Yes, but I am talking static friction, which allows the block to accelerate up to speed v_conveyor belt when it falls onto it.

If the block simply falls straight down onto the belt, it has zero velocity in the x direction. So when it falls onto the belt, it will pick up speed until the speeds match. So there has to be a net force acting on the block to cause it to accelerate. Thats what the static friction does. And that force acts for some amount of time, and over some distance. So it supplies some amount of work to the box.
There has to be some motion of the box relative to the belt. That means the friction is kinetic. I don't see how static friction could supply the accelerating force.

AM
 
  • #21
Andrew Mason said:
There has to be some motion of the box relative to the belt. That means the friction is kinetic. I don't see how static friction could supply the accelerating force.

AM
Till the box moves relative to the belt, the friction between them is kinetic. When the box moves together with the belt, the friction is static. If the belt starts to accelerate, the box will accelerate together with it if the force of static friction is enough to accelerate the box. The magnitude of the static friction is indefinite, it has only an upper limit. If this limit is higher than the acceleration times the mass of the box, the static friction will accelerate the box.

Can friction do positive work?

Put your hand on a sheet of paper on the table, and move your hand along the table: the sheet of paper will move together with your hand.
What are the forces exerted on the paper?
The vertical forces, gravity and the normal forces both from your hand and the table will cancel.
Horizontal forces are the static friction arising from the interaction between your hand an the paper, and the force of kinetic friction coming from the interaction between the table and the sheet. When the sheet (together with your hand) moves with constans velocity the forces of static and kinetic friction are of equal magnitude and as the force of kinetic friction is nonzero, so is the force of static friction.
The force of static friction between your hand and the sheet points forward, in the direction of motion. The force of kinetic friction between table and sheet points backwards.
Does the force of static friction exerted on the sheet of paper do work on the sheet? Yes. It is nonzero force, parallel to the displacement. Is this work, done by this force on the sheet positive? Yes, as the force points in the direction of displacement of the sheet.
So the force on static friction on the sheet of paper is POSITIVE here.

Work is defined in a certain frame of reference as done on a body by a force exerted on the body during the motion of the body. It is nonzero whenever the force and displacement have parallel components. It is positive if these parallel components point in the same direction. It has no sense to talk about work in general, without specifying frame of reference, force, and body acted on by the force.
As for the conveyor belt, seeing from the ground, the force of friction will accelerate the box dropped on it, so it means a positive work on the box. At the same time the friction means a resistive force exerted on the belt, opposite to the motion of the belt. So the work done by the force of friction exerted on the belt is negative. The summ of these works is negative, tending to decrease the mechanical energy of the whole system belt + box.

In the frame of reference moving together with the belt, you would see the box dropped onto the belt sliding on the belt and decelerating to full stop. The displacement of the box in this system is opposite to the force of friction, so the work done on the box by the friction is negative IN THIS FRAME OF RERERENCE.

ehild
 

What is friction and how does it work?

Friction is a force that opposes the motion of an object. It occurs when two surfaces come into contact and rub against each other. The force of friction is caused by microscopic irregularities on the surfaces of the objects, which create resistance and slow down the motion.

How does friction affect the total work of a system?

Friction reduces the amount of work that can be done by a system. As an object moves against a surface, friction converts some of the energy of motion into heat, which is dissipated and lost from the system. This means that the total work done by a system in the presence of friction is less than the work done in the absence of friction.

What factors affect the amount of friction in a system?

The amount of friction in a system depends on several factors, including the type of surfaces in contact, the force pressing the surfaces together, and the speed at which the objects are moving. Rougher surfaces, greater force, and higher speeds all result in higher friction.

How can friction be reduced in a system?

Friction can be reduced by using lubricants, such as oil or grease, to create a smooth layer between the surfaces. Another method is to use materials with low coefficients of friction, such as Teflon or ball bearings, to reduce the amount of contact between the surfaces. Additionally, reducing the force pressing the surfaces together or decreasing the speed of the objects can also decrease friction.

Can friction ever be beneficial in a system?

Yes, friction can be beneficial in certain situations. For example, friction allows us to walk without slipping, holds objects in place, and enables vehicles to stop. In some cases, friction can also be used to create useful forces, such as in brakes or clutches, or to generate heat in machines like engines or drills.

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